DALLAS—The Liberian man hospitalized in Dallas with Ebola died Wednesday, demonstrating the deadliness of the disease even in nations with advanced health-care systems, and the challenge of treating the virus when it isn’t identified as early as possible.

It was the first known death in the U.S. of an Ebola patient sickened in the West African outbreak, out of a total of six people with the deadly virus treated in the U.S. The case of Thomas Eric Duncan differed from the others; he was gravely ill by the time he was admitted...